The axisymetric laminar boundary layer unsteady flow along a continuously stretching cylinder immersed in a viscous and incompressible fluid is studied. The governing partial boundary layer equations in cylindrical form are first transformed into ordinary differential equations these equations are solved analytically using the optimal modified Homotopy Asymptotic method in order to get a closed form solution for the dimensionless functions f and è. The main object of this study is to investigate the effect of an unsteady motion of a stretching cylinder on the flow and heat transfer characteristics such as surface skin friction and surface heat flux.These characteristics have a direct effect on the quality of the final product of the fiber manufacturing and extrusion processes. Considerable effects were found for the dynamic parameter (γ), the curvature parameter (ρ) and the prandtl number (pr) on the velocity and the heat transfer.